Math guides

Learn the method behind the answer

Choose a topic, follow a worked example, and open the related calculator when you want an independent check.

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Build one idea on another

Build reliable number skills with fractions, mixed numbers, place value, and significant figures.

4 guides Algebra

Learn how equations, exponents, and operation rules work instead of memorizing isolated steps.

6 guides Trigonometry

Connect angles, the unit circle, trigonometric ratios, identities, degrees, and radians.

5 guides Logarithms

Understand logarithms as exponents, compare common and natural logs, and apply log rules correctly.

3 guides Number Systems

Explore scientific notation, irrational numbers, square roots, e, and the complex number system.

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Algebra The Quadratic Formula Understand where the quadratic formula comes from, what each term does, and how to use it without sign errors. Algebra The Discriminant Use the discriminant to classify quadratic roots and connect its sign to a parabola's intersections. Algebra Completing the Square Turn a quadratic expression into a perfect square, solve equations, and identify a parabola's vertex. Algebra Exponent Rules Learn the product, quotient, power, zero, and fractional exponent rules and the conditions that make them valid. Algebra Negative Exponents Interpret negative exponents as reciprocals, simplify expressions, and avoid the most common sign and zero-base errors. Algebra Order of Operations Evaluate expressions consistently using grouping, exponents, multiplication and division, then addition and subtraction. Arithmetic Simplifying Fractions Learn how to reduce a fraction using common factors and the greatest common divisor, with worked examples and checks. Arithmetic Improper Fractions and Mixed Numbers Compare improper fractions and mixed numbers, convert between the two forms, and choose the useful form for a calculation. Arithmetic Adding and Subtracting Fractions Add and subtract fractions by building a common denominator, then reduce the result with clear worked examples. Arithmetic Significant Figures Learn which digits are significant, how rounding rules differ for measurements, and how to report calculated results honestly. Logarithms Logarithms Understand a logarithm as an exponent, evaluate simple logs, and recognize the domain and base restrictions. Logarithms Natural Log vs Common Log Compare ln and log base 10, understand their notation, and choose the appropriate logarithm for a problem. Logarithms Logarithm Rules Apply product, quotient, power, and change-of-base rules while keeping logarithm domains valid. Number Systems Scientific Notation Write very large and very small values as a coefficient times a power of ten and calculate with them correctly. Number Systems Rational and Irrational Numbers Distinguish rational and irrational real numbers using fractions, decimal patterns, roots, and examples. Number Systems Euler's Number e Understand the constant e through continuous growth, limits, exponentials, and natural logarithms. Number Systems Square Roots and Irrational Numbers Simplify square roots, identify perfect-square factors, and understand when a root is irrational. Number Systems Complex Numbers Learn rectangular and polar forms, arithmetic, conjugates, modulus, and how complex numbers extend the real line. Number Systems The Imaginary Unit i Learn why i is defined by i squared equals -1, how its powers cycle, and how it solves negative-root equations. Trigonometry Degrees and Radians Compare degree and radian angle measure, convert between them, and choose the correct calculator mode. Trigonometry Why 180 Degrees Equals Pi Radians Derive the degree-radian relationship from circle circumference and arc length instead of memorizing it. Trigonometry Sine, Cosine, and Tangent Understand the three basic trigonometric functions through right triangles and unit-circle coordinates. Trigonometry Trigonometric Identities Learn the reciprocal, quotient, Pythagorean, and angle-sum identities and when they can be applied. Trigonometry The Unit Circle Read sine, cosine, tangent, signs, and reference angles from the unit circle.